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Realizations of kinetic differential equations.

Gheorghe Craciun1,2, Matthew D Johnston3, Gábor Szederkényi4

  • 1Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706-1325, USA.

Mathematical Biosciences and Engineering : MBE
|November 17, 2019
PubMed
Summary

This study investigates finding a chemical reaction network that generates a given system of polynomial differential equations, known as kinetic realization. It explores chemically relevant properties and offers constructive answers applicable to data fitting and dynamic behavior analysis.

Keywords:
kinetic equationsmass action kineticsreaction networksrealizationsreversibilityweak reversibility

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Area of Science:

  • Chemical Kinetics
  • Systems Biology
  • Computational Chemistry

Background:

  • Reaction networks with mass action kinetics generate polynomial differential equations.
  • Determining if a given system of differential equations can arise from a reaction network is a key challenge.

Purpose of the Study:

  • To determine if a kinetic realization exists for a given system of polynomial differential equations.
  • To identify if such realizations possess chemically relevant properties like detailed balancing or mass conservation.

Main Methods:

  • The study employs constructive mathematical approaches to address the existence and properties of kinetic realizations.
  • Analysis involves exploring the relationship between differential equations and underlying reaction network structures.

Main Results:

  • Provides constructive answers to the problem of finding kinetic realizations for systems of polynomial differential equations.
  • Demonstrates the possibility of finding realizations with specific chemically relevant properties.
  • Highlights applications in fitting differential equations to data and analyzing dynamic behaviors.

Conclusions:

  • The existence and properties of kinetic realizations are systematically investigated.
  • Results offer practical utility in systems biology and computational chemistry for model building and analysis.
  • The findings have implications for solving related mathematical problems, such as the existence of positive solutions to algebraic equations.